1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

LECTURE 4. THE NONSQUEEZING THEOREM AND CAPACITIES 27 found in some of the articles in Audin-Lafontaine [AL].) In the next lectu ...

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LECTURE 5 Sketch Proof of the N onsqueezing Theorem Suppose that ¢ : B^2 n(l) --+ Z(r) is a symplectic embedding. Its image lies ...

30 D. MCDUFF, INTRODUCTION TO SYMPLECTIC TOPOLOGY can often prove they exist for all other J.^2 That is exactly what we need her ...

LECTURE 5. SKETCH PROOF OF THE NONSQUEEZING THEOREM 31 Further when J = Jsplit the unparametrized moduli space M(A, J)/G is comp ...

32 D. MCDUFF, INTRODUCTION TO SYMPLECTIC TOPOLOGY the curves Cn converge (as point sets) to a union of several spheres, and the ...

BIBLIOGRAPHY [A] V.I. Arnold, Mathematical methods in classical mechanics, Springer-Verlag, Berlin, 1978. [AL] M. Audin and F. L ...

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Holomorphic Curves and Dynamics in Dimension Three Helmut Hofer ...

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!AS/Park City Mathematics Series Volume 7, 1999 Holomorphic Curves and Dynamics in Dimension Three Helmut Hofer LECTURE 1 Proble ...

38 H. HOFER, HOLOMORPHIC CURVES AND DYNAMICS preserving the volume form: LxD = 0. Here L xD. denotes the Lie derivative of D. in ...

LECTURE 1. PROBLEMS, BASIC CONCEPTS AND OVERVIEW 39 l. Given a closed hypersurface S in IR^2 n and Hamiltonians H and K having S ...

40 H. HOFER, HOLOMORPHIC CURVES AND DYNAMICS Definition 1.10. We call a smooth vector field X on a closed orientable three- mani ...

LECTURE 1. PROBLEMS, BASIC CONCEPTS AND OVERVIEW 41 Assume that Xis Reeb-like. Then, by definition, ixD = d>.. and ix>..&g ...

42 H. HOFER, HOLOMORPHIC CURVES AND DYNAMICS Observe that being tight or overtwisted is a property of 6. rather than ,. It is a ...

LECTURE l. PROBLEMS, BASIC CONCEPTS AND OVERVIEW 43 There is a priori the possibility that a Reeb-like vector field is simultane ...

44 H. HOFER, HOLOMORPHIC CURVES AND DYNAMICS • There exists a closed connected Riemannian surface ( S, j), a finite subset r of ...

LECTURE 1. PROBLEMS, BASIC CONCEPTS AND OVERVIEW 45 such that a parametrizes a punctured neighbourhood of z 0. Define ii: [O,oo) ...

46 H. HOFER, HOLOMORPHIC CURVES AND DYNAMICS This follows from the fact that every overtwisted contact form admits a con- tracti ...